The idea of SH is only ever invoked when someone who has been told that there is nothing else that medical science can do to help.
Which you seize upon as being a gap into which you can then insert your God, so we need to take into account who is bigging-up the spontaneous recovery as being potential divine intervention as opposed to the more rational 'not fully understood', and whether these claims are little more than anecdotes to start with.
Mrs G (now a community nurse until she retires next year) worked in hospital based oncology (particularly cancers of the neck/head/throat), and also cardiology, for a number of years so I just asked her about whether any of the professionally trained medical or nursing staff she had ever worked with over the years ever suspected divine intervention when someone did a little better than expected to the extent of seemingly recovering from a terminal/serious illness.
She says that even when some people did do a little better that their prognosis suggested, and here she says not many did, in these cases the prognosis is an estimate based on knowledge of the progress of the main condition and its treatment, where some remissions are a direct result of treatment, but as regards the gravelly/terminally ill there are often other secondary illness processes going and that if successfully treated, along with carefully managed pain control, can give the impression of a temporary improvement for a while.
However, she was quite clear that never once over many years was the idea of divine intervention ever raised by professionally trained staff in any formal case reviews as being a serious option, and went on to say that her view is that it would be unprofessional for trained staff to speculate in this way. She added that even colleagues who she knew were religious never ever went down the miracle route.
Mrs G also said that the reality is that those patients who are told (to use your turn of phrase) that 'there is nothing else that medical science can do to help' generally died in line with the estimate they were given, and that some died sooner due to the likes of infections or the effects or analgesia, and that even if professional medical and nursing staff might be surprised at the occasional unexpected resilience of some who are very gravelly ill they wouldn't speculate that divine intervention occurred and that generally speaking temporary improvements were exactly that - temporary.
Let's face it, if divine intervention was a real option we'd see some proper academic studies in peer-reviewed clinical publications confirming that there was empirical evidence that was best explained by a 'miracle' having happened - so, do you have any to hand?